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Nested Roots

Source: 2020 AMC 12A #13

January 31, 2020
2020 AMC 12A2020 AMCAMC 12AMC 12 AAMC

Problem Statement

There are integers aa, bb, and cc, each greater than 1, such that NNNca=N2536\sqrt[a]{N \sqrt{N \sqrt[c]{N}}} = \sqrt[36]{N^{25}} for all N>1N > 1. What is bb?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> 6<span class='latex-bold'>(A)</span>\ 2\qquad<span class='latex-bold'>(B)</span>\ 3\qquad<span class='latex-bold'>(C)</span>\ 4\qquad<span class='latex-bold'>(D)</span>\ 5\qquad<span class='latex-bold'>(E)</span>\ 6
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